1. Technical Field
This invention relates to a device for performing wideband digital spectrometry, and more particularly, to a wideband digital spectrometer including circuitry that functions to utilize the inherent properties of the Walsh functions which take on only values of +1 or -1, in combination with a Walsh Fourier transform of power components obtained from the known Walsh Fourier amplitude transform, to achieve a simplified method of producing the Fourier power spectrum of an input signal.
2. Description of the Prior Art
In the past, two methods have been used to obtain the power spectrum of radio astronomy signals. The analog signal itself was often directly Fourier transformed to obtain the power spectrum desired, and more recently, the analog signal was converted to digital form and an autocorrelation performed on this digital representation to obtain the desired power spectrum.
In the analog method, the input signal is fed into a bank of bandpass filters with specified center frequencies and narrow bandwidths. These high Q filters are extremely difficult to manufacture and their accuracy is often restricted by the physical limitations of the filter components. To obtain the Fourier transform, each filter has to be followed by a rectifier and integrating device. If the filter bandwidth and integrator gains are not stable, the filter bank has to be continuously calibrated. The filter spacings and bandwidths cannot be readily changed, hence, the frequency resolution of the system is fixed upon construction.
The digital correlation techniques make use of the well-known Weiner-Khintchine theorem, which states that the power spectrum of a signal is the Fourier transformation of its autocorrelation function. One example of such a technique is discussed in "A 1024-Channel Digital Correlator" by J. G. Ables et al in Review of Scientific Instruments, Vol. 46, No. 3, March 1975 pp. 284-95. In this case, the correlator is built in four quadrants, allowing it to be used as four independent 256-channel correlators, two 512-channel correlators or one 1024-channel correlator when high resolution is required. The correlator is connected on-line to a computer, which obtains the Fourier spectrum in real time. This method, however, is limited, physically, to slow sampling rates, even when using the fast Fourier transform, due to the number of multiplications involved.
A higher sampling rate has been achieved in another autocorrelator, the construction of which is discussed in the article "A High Speed Digital Autocorrelation Spectrometer for Millimeter Astronomy" by C. Pell and L. T. Little in Journal of Physics E, Vol. 8, No. 9, 1975, pp. 786-789. In C. Pell et al, the sampling rate has been increased from 20 MHz for the Ables et al design to 60 MHz. This increase is achieved by using Schottky clamped TTLs in the computer. This technique, however, is still limited by the number of fast Fourier transform multiplications that must be performed.
Knowledge of the relationship between Walsh functions and Fourier functions is well represented in the prior art. One article, "Applications of Walsh Functions in Communications" by Henning F. Harmuth in IEEE Spectrum, November 1969, pp. 82-91 discusses the general application possibilities of Walsh functions, and more specifically, the advantages of Walsh-based digital filters.
Another article, "Application of Walsh Functions to Transform Spectroscopy" by J. E. Gibbs and H. A. Gebbie in Nature, Vol. 224, 1969, pp. 1012-1013, narrows the application of Walsh functions to the field of spectrometry without, however, discussing any specific means for actual implementation of the Walsh functions.
The problem remaining in the prior art is to provide a means for utilizing the Walsh function capabilities in conjunction with the preexisting techniques of digital spectrometry, to obtain a more efficient digital spectrometer.